Abstract
Abstract In this paper we deal with positive singular solutions to semilinear elliptic problems involving a first-order term and a singular nonlinearity. Exploiting a fine adaptation of the well-known moving plane method of Alexandrov–Serrin and a careful choice of the cutoff functions, we deduce symmetry and monotonicity properties of the solutions.
Highlights
The aim of this work is to investigate qualitative properties of singular solutions of semilinear elliptic problems involving a first-order term and a singular nonlinearity
In this paper we deal with positive singular solutions to semilinear elliptic problems involving a firstorder term and a singular nonlinearity
In the proof of Theorem 1.1 we develop a careful adaptation of the moving plane method that is quite recent, in order to deal with singular solutions of semilinear elliptic problems driven by the classical Laplacian operator
Summary
The aim of this work is to investigate qualitative properties of singular solutions of semilinear elliptic problems involving a first-order term and a singular nonlinearity. In the proof of Theorem 1.1 we develop a careful adaptation of the moving plane method that is quite recent, in order to deal with singular solutions of semilinear elliptic problems driven by the classical Laplacian operator. To the best of our knowledge, Theorem 1.1 is new and extends some of the results contained in [26, 39] to the case involving first-order terms This technique is so powerful and flexible that covers the following cases: unbounded sets [26, 39], the p-Laplacian operator [27, 36], double phase operators [7], cooperative elliptic systems [8, 9, 25], the fractional Laplacian [37] and mixed local-nonlocal elliptic operators [10]
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